Deform geometry along spline in Animation Nodes
First, you normalize the vertices positions into a unity setting. This is easily done by subtracting the lower-left-forward corner position of the bounding box and dividing by the difference between the upper-right-backward corner position and the lower-left-forward corner position of the bounding box as follows:



You will notice that the vertices are now in a cube located at the origin with length, width, and height of unity. Next, we choose an axis to evaluate the spline at, I will choose the x axis, because I want the cylinder to be deformed along that axis. I will then use the values of that chosen axis to evaluate the spline. We scale the tangent and cotangent based on the values of the other two axis (y and z because we chose x), add the result, and add the evaluated location on top of that as follows:



Want to center it? Just subtract 0.5 from the normalize locations:



You can compute the lower-left-forward and upper-right-backward bounding box points manually from a list of points using the following node tree: